They suggested I can use Yapily (https://www.yapily.com/) in some cases, but the documentation for that says I need to be FCA registered. All I want is an API for my bank account, not the bank account of anyone else.
Am I missing something here?
You could try using TrueLayer (which is FCA certified) as a proxy. Alternatively, switch to a bank like Starling or Monzo which allow you to create an access token for your own account.